calculate circle sector

[Bloody_geek]

Hey there

I'm developing a little application in windows, where you can calculate the properties of a circle with two given values.
Possible values: radius, angle, arc length, circular yearn, arc, area.
I got some problems calculating the circle in the following two cases: "circular yearn and arc given" and "arc and area given"

I have no clue how to integrate the calculations into my code or even calculate the properly at all.
My only guess is that I have to do a numeric calculation but I have no idea how to manage this.

ps: I'm using tkinter, mpmath and sympy

I'm greatfull for any hint!

greetings